Abstract #300207

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JSM 2003 Abstract #300207
Activity Number: 233
Type: Topic Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Business & Economics Statistics Section
Abstract - #300207
Title: Maximum Likelihood Estimation of a Class of Continuous-Time Long-Memory Processes
Author(s): Henghsiu Tsai*+ and Kung-Sik Chan
Companies: Academia Sinica and University of Iowa
Address: Institute of Statistical Science,, Nankang, Taipei, 115, Taiwan
Keywords: CARFIMA models ; fractional Brownian motion ; innovations algorithm ; irregularly spaced data ; polynomial trend
Abstract:

We develop a new class of Continuous-time Auto-Regressive Fractionally Integrated Moving-Average (CARFIMA) Models that is based on the stochastic calculus for fractional Brownian motions recently developed by Duncan et al. (2000). This new class of models is useful for modeling regularly spaced and irregularly spaced discrete-time long-memory data, as well as studying the underlying autocorrelation and spectral structure. We prove a set of necessary and sufficient conditions for the stationarity of the model and derive the autocovariance function of a stationary CARFIMA process. Maximum likelihood estimation of the CARFIMA model with discrete-time data is implemented via the innovations algorithm. The empirical performance of the maximum likelihood estimator is studied by simulation. We derive some large sample properties of the maximum likelihood estimator, and illustrate the new approach with a real dataset from an environmental study.

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